To add these radicals together their radicands must be the same:

8\( \sqrt{12} \) + 6\( \sqrt{3} \)
8\( \sqrt{4 \times 3} \) + 6\( \sqrt{3} \)
8\( \sqrt{2^2 \times 3} \) + 6\( \sqrt{3} \)
(8)(2)\( \sqrt{3} \) + 6\( \sqrt{3} \)
16\( \sqrt{3} \) + 6\( \sqrt{3} \)

Now that the radicands are identical, you can add them together:

A rational number (or fraction) is represented as a ratio between two integers, a and b, and has the form \({a \over b}\) where a is the numerator and b is the denominator. An improper fraction (\({5 \over 3} \)) has a numerator with a greater absolute value than the denominator and can be converted into a mixed number (\(1 {2 \over 3} \)) which has a whole number part and a fractional part.

To multiply fractions, multiply the numerators together and then multiply the denominators together:

\( \frac{1}{6} \) x \( \frac{3}{5} \) = \( \frac{1 x 3}{6 x 5} \) = \( \frac{3}{30} \) = \(\frac{1}{10}\)

The first few multiples of 2 are [2, 4, 6, 8, 10, 12, 14, 16, 18, 20] and the first few multiples of 6 are [6, 12, 18, 24, 30, 36, 42, 48, 54, 60]. The first few multiples they share are [6, 12, 18, 24, 30] making 6 the smallest multiple 2 and 6 have in common.

A factor is a positive integer that divides evenly into a given number. For example, the factors of 8 are 1, 2, 4, and 8.